Numerical Solutions for Diffusion and nth-Order Chemical Reactions in Isothermal Catalytic Pellets

2003 ◽  
pp. 483-490
Keyword(s):  
Chemical Reactions ◽  
Numerical Solutions

scholarly journals Effects of Exothermic/Endothermic Chemical Reactions with Arrhenius Activation Energy on MHD Free Convection and Mass Transfer Flow in Presence of Thermal Radiation

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Kh. Abdul Maleque
Keyword(s):  
Activation Energy ◽  
Mass Transfer ◽  
Differential Equations ◽  
Thermal Radiation ◽  
Chemical Reactions ◽  
Numerical Solutions ◽  
Porous Plate ◽  
Local Similarity ◽  
Shooting Methods ◽  
Arrhenius Activation Energy

A local similarity solution of unsteady MHD natural convection heat and mass transfer boundary layer flow past a flat porous plate within the presence of thermal radiation is investigated. The effects of exothermic and endothermic chemical reactions with Arrhenius activation energy on the velocity, temperature, and concentration are also studied in this paper. The governing partial differential equations are reduced to ordinary differential equations by introducing locally similarity transformation (Maleque (2010)). Numerical solutions to the reduced nonlinear similarity equations are then obtained by adopting Runge-Kutta and shooting methods using the Nachtsheim-Swigert iteration technique. The results of the numerical solution are obtained for both steady and unsteady cases then presented graphically in the form of velocity, temperature, and concentration profiles. Comparison has been made for steady flow () and shows excellent agreement with Bestman (1990), hence encouragement for the use of the present computations.

Exact and numerical solutions to the system of the chlorite iodide malonic acid chemical reactions

2021 ◽  
Vol 41 (1) ◽  
Author(s):  
S. T. R. Rizvi ◽  
Aly R. Seadawy ◽  
S. O. Abbas ◽  
S. Latif ◽  
Saad Althobaiti
Keyword(s):  
Chemical Reactions ◽  
Malonic Acid ◽  
Numerical Solutions

Surface reactions observed by photoemission electron microscopy (PEEM)

1992 ◽  
Vol 50 (1) ◽  
pp. 286-287
Author(s):  
H.H. Rotermund
Keyword(s):  
Electron Microscopy ◽  
Electron Microscope ◽  
Work Function ◽  
Chemical Reactions ◽  
Reaction Diffusion ◽  
Dynamic Processes ◽  
Clean Surface ◽  
Crystal Surfaces ◽  
Single Crystal Surfaces ◽  
Photoemission Electron

Chemical reactions at a surface will in most cases show a measurable influence on the work function of the clean surface. This change of the work function δφ can be used to image the local distributions of the investigated reaction,.if one of the reacting partners is adsorbed at the surface in form of islands of sufficient size (Δ>0.2μm). These can than be visualized via a photoemission electron microscope (PEEM). Changes of φ as low as 2 meV give already a change in the total intensity of a PEEM picture. To achieve reasonable contrast for an image several 10 meV of δφ are needed. Dynamic processes as surface diffusion of CO or O on single crystal surfaces as well as reaction / diffusion fronts have been observed in real time and space.

Microwaves: Application in Electron Microscopy

1990 ◽  
Vol 48 (3) ◽  
pp. 140-141
Author(s):  
Anthony S-Y Leong ◽  
David W Gove
Keyword(s):  
Electron Microscopy ◽  
Light Microscopy ◽  
Chemical Reactions ◽  
Electromagnetic Waves ◽  
Tissue Fixation ◽  
Primary Method ◽  
Dipolar Molecules ◽  
Wide Range ◽  
Time Required ◽  
Cryostat Sections

Microwaves (MW) are electromagnetic waves which are commonly generated at a frequency of 2.45 GHz. When dipolar molecules such as water, the polar side chains of proteins and other molecules with an uneven distribution of electrical charge are exposed to such non-ionizing radiation, they oscillate through 180° at a rate of 2,450 million cycles/s. This rapid kinetic movement results in accelerated chemical reactions and produces instantaneous heat. MWs have recently been applied to a wide range of procedures for light microscopy. MWs generated by domestic ovens have been used as a primary method of tissue fixation, it has been applied to the various stages of tissue processing as well as to a wide variety of staining procedures. This use of MWs has not only resulted in drastic reductions in the time required for tissue fixation, processing and staining, but have also produced better cytologic images in cryostat sections, and more importantly, have resulted in better preservation of cellular antigens.

Atomic Imaging of Crystals using Large-Angle Electron Scattering in STEM

1990 ◽  
Vol 48 (1) ◽  
pp. 74-75
Author(s):  
D.E. Jesson ◽  
S. J. Pennycook
Keyword(s):  
Wave Function ◽  
Electron Scattering ◽  
Numerical Solutions ◽  
Large Angle ◽  
Real Space ◽  
High Angle ◽  
Analytical Treatment ◽  
Order Zero ◽  
Experimental Conditions ◽  
Ewald Sphere

It is well known that conventional atomic resolution electron microscopy is a coherent imaging process best interpreted in reciprocal space using contrast transfer function theory. This is because the equivalent real space interpretation involving a convolution between the exit face wave function and the instrumental response is difficult to visualize. Furthermore, the crystal wave function is not simply related to the projected crystal potential, except under a very restrictive set of experimental conditions, making image simulation an essential part of image interpretation. In this paper we present a different conceptual approach to the atomic imaging of crystals based on incoherent imaging theory. Using a real-space analysis of electron scattering to a high-angle annular detector, it is shown how the STEM imaging process can be partitioned into components parallel and perpendicular to the relevant low index zone-axis.It has become customary to describe STEM imaging using the analytical treatment developed by Cowley. However, the convenient assumption of a phase object (which neglects the curvature of the Ewald sphere) fails rapidly for large scattering angles, even in very thin crystals. Thus, to avoid unpredictive numerical solutions, it would seem more appropriate to apply pseudo-kinematic theory to the treatment of the weak high angle signal. Diffraction to medium order zero-layer reflections is most important compared with thermal diffuse scattering in very thin crystals (<5nm). The electron wave function ψ(R,z) at a depth z and transverse coordinate R due to a phase aberrated surface probe function P(R-RO) located at RO is then well described by the channeling approximation;

Fine structure and properties of defects in naturally occurring silicates and oxides

1990 ◽  
Vol 48 (4) ◽  
pp. 460-461
Author(s):  
David R. Veblen
Keyword(s):  
Chemical Reactions ◽  
High Resolution Electron Microscopy ◽  
Extended Defects ◽  
Single Chain ◽  
Naturally Occurring ◽  
Resolution Electron ◽  
Fine Structures ◽  
Image Simulations ◽  
Similar Crystal Structure

Extended defects and interfaces control many processes in rock-forming minerals, from chemical reactions to rock deformation. In many cases, it is not the average structure of a defect or interface that is most important, but rather the structure of defect terminations or offsets in an interface. One of the major thrusts of high-resolution electron microscopy in the earth sciences has been to identify the role of defect fine structures in reactions and to determine the structures of such features. This paper will review studies using HREM and image simulations to determine the structures of defects in silicate and oxide minerals and present several examples of the role of defects in mineral chemical reactions. In some cases, the geological occurrence can be used to constrain the diffusional properties of defects.The simplest reactions in minerals involve exsolution (precipitation) of one mineral from another with a similar crystal structure, and pyroxenes (single-chain silicates) provide a good example. Although conventional TEM studies have led to a basic understanding of this sort of phase separation in pyroxenes via spinodal decomposition or nucleation and growth, HREM has provided a much more detailed appreciation of the processes involved.

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